The replicated typo blog has two great posts summarizing the current state of animal cognition research. You might remember that I blogged about this from a personal, and also a more “philosophical” point of view… using the possibility that animals have similar feelings to us to argue for vegetarianism.

The broad brush is that animals pass most of the tests that humans do:

“1. Mirror self-recognition

2. Tests of metacognition;

3. Metacognition of others’ mental states”

Mirror self-recognition is the realisation that the animal in the mirror is really you. This test has now been passed by a wide range of species: “including the great apes (chimpanzees, bonobos, orangutans, gorillas), but also elephants, dolphins and magpies (Blackmore 2010: 210-214)”. Humans pass this around age 3.

Metacognition means having an understanding of your own thought process. The standard lab-test would be whether you know that you know something, tested by a reward system for getting a question right, or a lesser reward declining to answer. Many higher primates seem to pass this test.

The final test is the understanding that others may or may not know something. On this the results are ambiguous. Chimpanzees definitely know whether another chimp may know something, e.g. you can only steal some food if the head honcho doesn’t know about it. But they only partially pass other tests, and perform worse than humans.

So basically, “animals other than humans are conscious and have subjective experiences that rely on some degree of consciousness” (Burkhard & Bekoff 2009: 42).

(All quotes and references are taken from the replicated typo blog and you should go there for the full story).

Saw some awesomely scary ant action at the weekend. When I arrived, this worm was still wriggling:

Before...

When we returned from our walk, this is what remained:

and after.

Very clearly, these ants have swarmed the worm when it was stranded on the paving and attacked it so ferociously that it could not escape. They seem to have sucked out all the juices leaving a dry husk. As I watched, I could not see the ants that left the worm taking anything away – it must have all been stored inside their bodies.

I don’t really know anything about what sort of ant these are, and whether they always feed like this, but it was a rare treat to see such a coordinated assault on a creature hundreds of times their size. I’m really very glad that there are no ants close to 100th the size of me – though I’d still take these guys over ArmyAnts..

PS Apologies for the poor quality phone pics, we forgot to take our real camera out this weekend.

I was very excited to discover the work of Peter Singer, a philosopher and vegetarian who has been very active from the eighties till the present day. Everyone with an interest in the subject should read his interesting article Utilitarianism and Vegetarianism, a good discussion piece that engages with the philosophical arguments both for, and against, eating meat (although Singer has very clear views). It is a response to criticism of his earlier philosophical look at the Animal Liberation Movement. The most gratifying thing for me is that is argument is almost identical to my discussion on the subject, which were not based on any philosophical tradition but formed simply from an attempt to be rational, honest and consistent in my moral viewpoint. The essence of both arguments is utilitarianism.

Utilitarianism is a moral philosophy that argues that we have a moral imperative to maximise the total “utility” in the world. Each person gains utility from things they like or want, such as food, money, happiness, fulfillment, comfort, pleasurable company, etc, and how important each thing is obviously depends on what else you have. Books and art are no good if you are starving, but are important once your tummy is full. Utility is of course a fuzzily defined thing, and could alternatively be called “value”. Importantly, utilitarianism acknowledges that not all people view all things as equally important – each will have preferences, and these should dictate how things should be shared out. For example, if me and a friend have two apples and two chocolate bars, and I like apples and he chocolate bars, then we should not share them equally – I should get two apples and he two chocolates. If only all moral problems were this simple.

For the utilitarian, how something happens doesn’t explicitly matter – only the end result counts. An example may help distinguish utilitarianism from competing philosophies at this point – let us consider the hero/villain problem. In scenario 1, imagine you are faced with a burning building and have two options: to save three children from one room, or to save an old man from another. Almost everyone would agree that the correct “heroic” thing to do is to save the children. Now in scenario 2 you are a prisoner, and your captors insist that you either shoot three children, or an old man. If you do not, they will kill all four. Many people will see this as a true moral dilemma, because you are a “villain” no matter what you do. You have moral responsibility for their death, even though you couldn’t prevent it. Yet isn’t the outcome exactly the “same” in both scenarios?

Such an argument has no doubt been used to undermine the utilitarianism philosophy, but the analysis is not complete. The outcome only the same if we count only deaths at the end; it does not take into account the whole of the utility function. We often “value” (gain utility from) taking a positive action to help others, and additionally we lose utility when forced to hurt others. So the two scenarios are not the same because the total utility in both is different. Although my example is unambiguous enough so that most people would still spare the children, some people would refuse to kill anyone, therefore removing the blame of the deaths from themselves. More people would die, but the total utility might still be higher because the blame for the deaths falls squarely on the captor, rather than with yourself.

So this brings me in a roundabout way to the point of this post – that we need to view utility in a very inclusive manner. Both Singer, and myself, argue in detail that all beings that are capable of having goals, motivations, happiness or discomfort should be part of the equation. We do not claim that all opinions are equal – just that all are there for consideration. As Singer puts it, “many nonhuman animals can experience pain and pleasure… in this respect they are like humans and unlike rocks”. We don’t have to care about rocks, buildings or ice sheets. But we do have to care about all animals and plants and people, and weight their preferences accordingly. (Note that this results in having to care about rocks and buildings and ice sheets, but for different reasons).

Singer puts the point across very clearly, in conjunction with some contemporary objections. Central to the argument is that we move away from a “rights” based view of morality towards one that balances all preferences fairly. I still need to delve further into the literature to expose this fully, but the logic seems sound: rights only place rough bounds on what people can and can’t do, whereas utilitarianism allows for a much more detailed resolution of conflict. It also allows (he argues that it insists) for varying degrees of importance to be placed on different individuals, therefore allowing animals to be protected on the same basis as people, but to a lesser degree. I think almost everyone will agree that some account should be placed on animal preferences; that some attempt should be made to prevent them suffering and to have some degree of comfort and freedom; the only issue is how much.

We both agree that utilitarianism implies that circumstances should determine what is OK; there are no absolutes. Eating meat is fair enough if you are on the brink of starvation; the line moves and is more blurry in normal life. He is usually vegan but will eat vegetarian food at others houses, for example. Presumably for Singer the social discomfort of making others cook completely out of their comfort zone is too much when balanced against eating dairy produce. I tend to agree; such issues can in some cases result in weaker friendships.

As far as I can see so far, the debate hasn’t moved on much. Read his work, and the responses to his work, and try to place your own views in the argument. I will try to do so and I’ll post back here with my conclusions.

There is much discussion about whether to vote yes, or no. Most of it focusses on the short term impact – how seats won would change in the new system if people kept their voting habits. This misses the point. More astute observers note that whether people support “yes” or “no” depends on how their preferred party will benefit. This is true, but somewhat beside the point – we should choose a system that gives the best outcome, not the one that favours us.

An important, and somewhat overlooked implication is that the Alternative Vote (AV) system would allow people to vote honestly. This means that candidates can be ranked by the order an individual wants. This is not true in the current “First Past the Post” (FPTP) system, where many people are forced to vote tactically. If you want your vote to count, you have to pick your favoured option from the two candidates you predict to do best. This prediction leads to a very nasty feedback – the two leading options in public opinion (usually the top two from the last vote) get a disproportionate share of the vote. This is bad for the system in general because votes do not correspond to public opinion. The more we can tell the politicians about what we want, the better they can represent us. So we should prefer a voting system that allows us to be honest.

Even worse, it leads to political lock in – the parties who did best in the past will do best in the future, irrespective of their policy. This permits leading parties to interpret a vote for them as a support for their policies, when in fact most voters may disagree with the majority of such policies. (Though more than the competing party…) This lets policies with little public support be pushed through… the Iraq war being seen as “supported” due to Labour’s re-election is one example of this, as is the Tory University reform.

(As a side point, AV may result in increased participation in voting. If you know that your vote will be counted, even if it not for one of the major parties, then you are more likely to bother.)

That is why I’ll be voting “yes”.

PS No doubt the AV system will have its own problems, but the current system seems unjustifiably broken to me. I’d particularly welcome comments explaining how FPTP is not broken in the sense above.

The reality of human interactions is that we fear and avoid what we don’t understand. Most conscious thought about culture is about differences: “we” have this way of doing things, “they” do something else. This affects all interactions in a fundamental way. Similar cultures will mix more, trade more, share more than distant cultures.

But culture is more than a way of being – it affects the way people interact in and behave very deep ways. Turchin’s theory of civilization says that Asibiya – the ability for group action – builds up exactly on the borders between cultures. This is because the definition of “us” becomes very clear when contrasted to a very different “them”. It’s a nasty fact of humanity that people can show great altruism and kindness to others, yet on an everyday level it is often nepotism – aggression towards people out of your group – that rules. The origin of states arises from small tribes lies that form strong bonds – which is precisely what Asibiya is designed to explain.

Culture and religion are integrally related, and religion is an aspect of culture that kingdoms have some reasonable control over. Although switching between Christianity and Muslim faiths has been a long and painful process for many nations, religions can splinter off and yet remain fundamentally the same thing to the peasantry. Protestantism appeared mostly as a response to Catholic domination and attempts to influence politics. Although almost the same faith, the differences create a strong “us and them” feeling in people – at least the nobles – that allows wars to be justified and alliances forged. Yet both are “us” when compared to their more different neighbours – Muslims, or the Sikhs, or the Jews.

Differences in religion and culture in general control what is acceptable and unacceptable in war, whether the enemy is just an ally with the wrong king, or an inhuman devil. What do the populace think of the king burning an enemy city? If there is little shared culture with the city then people will be content, possibly even happy to see the influx of “free” goods and slaves. But if people know people of the persecuted culture, trade there, visit there on pilgrimage or have a religious empathy for them, then they will object, strongly. In ancient times, warfare often resulted in the burning of cities and the taking of slaves. Conversely, during the late middle ages (and most civil wars) the European nobility fight each other – and people do die – but cities go on much as they always had because nobody would benefit from harming the people.

Since culture moves with people, and people do not move homogeneously but in waves, displacing those who have gone before them. On the front of this wave is always a new technology or way of life, and with it associated a very different way of being from those on the other side of the divide. Further (more historical) examples are the Roman expansion into the barbarian lands, the American conquest, the formation of Russia and of Australia, and of China (during multiple periods). These waves do not grow forever, but they do leave cultural borders at which Asibiya can grow due to the added pressures of living in proximity to a strange and dangerous culture.

Living on a cultural border is both a very dangerous, and potentially very rewarding. Almost all great empires are formed there, and the mixture of cultures allows each to take on a form very distinct from its origins. Examples abound, and counterexamples are hard to find – Egypt, China, Greece, Rome, the Islamic empire, Russia, Britain, America – all were forged on the borders of the strongest empires of the previous era, and most often on the border at which the largest cultural differences occurred.

Culture is also important as a way of spreading change within established groups, not just in forming nations. Money, writing, mapmaking, shipbuilding, architecture – all these and more ideas can be exported through the movement of people that use them. It also shapes how people interact and function in everyday lives. Successful ideas spread on the back of cultural diffusion, and to take them in, an empire must also import the aspects of culture associated with them. Just look at how American business – and in parallel it’s culture – exported throughout the world today.

Relation to civilization

This leads to a clear dynamic for culture in civ interactions: the magnitude of trade and other agreements depends on the degree of similarity between the two cultures. It really is better to be at war with distant heathens than your neighbours because of the lost revenue, and the disapproval of your subjects.

An important dynamic can be that the presence of a very different other on the border will unite people to a degree – they have more motivation to be united. But the same force can quickly flip to work in reverse – if an empire is very large and unstable, then a new and dynamic culture may form from the fusion of two very dissimilar ones, rebelling from their host empires and – if initially successful – able to gather momentum at a pace that will lead to their rapid ascension as the new power.

Cultures that interact will be exchanging people, culture and ideas, and will become similar according to how strongly this occurs. The deliberate adoption of an imported technology will come at the cost of imported culture – a dynamic that enables cultural victory by exporting your nations ideas to the world. And conversely, the collapse of an empire that has already exported much culture is not so catastrophic because in its ashes lie the shared cultural bonds that will enable the pieces to be picked up, and will find itself in a far more familiar world.

As before, this needs to be implemented as a genuine dynamic that can form part of a player’s strategy. It will probably correspond to the creation of a new cultural group – the fusion between the two original groups – that can pick and choose the cultural traits that are most suitable for the current times. In a sense, it is more likely that religion be created from such a succession than a religious movement will cause a succession to happen – the historical examples of Christianity and Islam both indicate that a lot of similar thought was around in the time period. They both found success by exporting cultural values that were successful.

Successful civilisations throughout history have grown rapidly, appearing unstoppable. Some (like Rome, and Han China) existed stably for hundreds of years. Others, like Alexander the Great‘s Asian Empire did not. But in every kingdom, empire and state that has ever existed (excluding the few surviving today, which are probably not as eternal as we’d like to think), something has eventually changed. Once great empires are defeated by a smaller rival (e.g. Sassanid Persia), and others crumble all by themself. Changing fortunes are one of the clearest signals in history.

Yet we have no mechanistic understanding for the collapse phenomenon. It is entirely absent from “Vanilla” Civilization, which assumes that growth gives power and power allows further growth, with the result that empires grow at an “exponential” rate. This is a good first approximation: over time, population has grown exponentially as more people plant more food which feeds more people. The same applies to technology, and social development. Yet these trends clearly do not apply to states and empires, even though it is often within the largest states that population density, technology and social development are highest. So why do empires fall?

There are many mechanisms in history that may cause the strong to become weak. Perhaps their strength was illusory. Since success at war pays well in the short term, winners of scuffles can hire more soldiers and thus will get greater military strength. But if the infrastructure for effective taxation, trade and public works to support the empire is not in place, when the expansionist wars stop (as they must) the empire will be overstretched. Warlords from within or without the empire can take over distant provinces and the empire collapses. Conversely, smaller civilisations are more efficient and competitive per person, people are more involved in the state, greater mobilisation is possible and they have unity of purpose.

Yet these stories are just that – stories. When does the first apply, leading to large states conquering small, and when do the small states gain an upper hand?

Modifications to Civilization such as “Revolution” and “Rhys and Fall of civilisation” both make a good attempt at adding this dynamic. The basic idea is that civilizations that are large (relative to what their infrastructure and governmental system can handle) will experience both inefficiency and stability problems. This is basically correct – but is added as a fudge, entirely without a mechanism. Some large empires (China for example) have managed to avoid internal strife (or at least, it hasn’t lasted all that long). Yet other, similarly sized empires collapsed almost without trace. What is the difference?

Peter Turchin has some ideas – he says that societies have “asabiya” – a unity of purpose that allows for collective action. Groups of people that live together in strife (such as desert nomads) – and particularly those on cultural divides – develop strong bonds and are able to commit very strongly to struggles. This allows these small groups to conquer much larger states, because the groups with such states defect and bicker and are not willing to die for their cause.

Once in power, the asibiya of such a group declines as the need for collective action decreases, and the lure of luxuries increases. The powerful state weakens to be eventually taken over by a smaller, more dedicated group. See his book “Historical Dynamics: Why States Rise and Fall” and his later books and his webpage for ideas, which stem from the works of the 15th century Arabic scholarIbn Khaldun.

There is clearly something to this theory, but it is incomplete as it stands. Did 18th century England have higher asabiya than 18th century Venice (or Germany for that matter)? It is impossible to tell. Clearly, England was on the rise in a way that Venice wasn’t, but we can’t measure asabiya. The small nomadic groups described by asabiya are not in play here; there are more standard, more economic and sociological forces. What are they?

Essentially, we don’t know yet. I’ve been involved in some modelling, where we show that treating a state as a number of semi-independent groups can lead to this dynamic. Each group is coerced into the state, but gains benefits from being a part of it. Whilst everyone is on board, everything is fine – culture and development increase, and great achievements are made by the elite. But the groups at the bottom of the pile get a worse and worse deal – because they have less political power, and political power tends to lead to more political power. When one group rebels, the benefit to the rest is reduced, and it can set off a chain reaction leading to state collapse.

The model allows groups to act in an entirely selfish way – there is no fluffy concept of asabiya, but asabiya arises as a natural result of within-group competition. It is nice for several reasons. Empires that look strongest from the outside – those with high development and culture – are exactly the least stable. Collapse can be triggered internally, or by external stresses such as war. These problems can all be overcome by continualgrowth of the state, so that everyone is getting a better deal… but no growth is forever.

Unfortunately, the only reference for this is a Masters Student thesis. But watch this space…

Relation to civilization

The implication for the modelling of artificial societies is that group dynamics matter. Giving people a shared identity leads to greater capacity for action – but this shared identity is eroded by distance in culture, status, religion, nationality, money and power. Each new realisation of a state can form its identity on new grounds – by language, or religion, or race, or ideology, shared suffering or shared experience. This is why modern states have had to be more inclusive, to create a shared identity amongst people who in other circumstances would see themselves as very different.

This implies that there is a natural lifecycle to states. It is not necessary for a state to collapse and be rebuilt, but the people must find a new way of feeling unified. The natural dynamic in a game is to have groups with identities that are shared to a greater or lesser extent, and that have different desires based on these. Weaker groups will be less able to bargain for their desires and therefore will want to rebel… leaders have the option of silencing them, but at the cost of alienating further groups. It is not a long term strategy to kill your own citizens, and eventually, the state must be restructured, perhaps smaller, to create a new shared identity and (most importantly) a more even distribution of power. The greater the change, the more dramatic the collapse will be. Making demands of citizens – such as drafting for war – or not protecting them adequately will result in rebellion of some groups, leading to the rebellion of more.

It is important to make this a dynamic that is visible, rather than spawning random rebellions that just happen because some counter got too high. The groups within the empire should be visible, broken down by town, and each one should be unique in some way. Groups can be absorbed when their needs coincide strongly, which will be most common during rebellions or redefining of statehood. They cause trouble only when their needs are not met – be they financial, political, or religious. They can be eliminated by force – at the cost of scaring other groups – or be brought in line through education or incentives. Left alone, strong groups will get stronger and weak ones weaker, at a rate that depends on the degree of accountability in the society. Therefore different types of government will have a different ability to cope with differing needs.

Differences between groups are defined in terms of differences within the state versus differences without. If there is a clear enemy, people will remain united. Diasporas will lead to shared demands over multiple states, but also lead to shared bonds and greater trade of both goods, knowledge and cultural values. Multiple cultures within a state lead to less focus but greater rates of innovation and cultural growth.

Adding this one feature will in one swipe unite the process of cultural diffusion (to be dealt with later) with the internal process that causes collapse. “All” that remains to be done is to implement the mechanic in a balanced way that is interesting to engage with and produces realistic effects…

I need to make two confessions. Firstly, in my “youth” I have been just a little addicted to the “Sid Meier’s Civilization” series of games. Secondly, I have since been thinking very deeply about history – deep enough that I have supervised a Master’s Project studying the processes that allow civilisations to rise, and fall. Over the next few weeks, I’m going to write several posts distilling my thoughts, with each split into:

Some aspect of history that has an interesting and dynamic pattern;

How this might relate to “simulations of history”, i.e. civilization. This part of the post will mostly only be of interest for those also needing a visit to Civilization Anonymous (after just one more turn!).

This is an introduction and index; I will update each topic below with the correct link when they are published. The posts will start out well researched with academic references at the bottom and web links in the text; towards the end of the series my “expert knowledge” will wane.

Introduction

It has been claimed that history is just “one damn thing after another“. Certainly history is extremely complex, and there are almost no examples where there is a simple cause and effect for large-scale events. But that does not mean that there are no patterns to be found. Broad generalisations about the human psyche are possible when modern experimental psychology, sociology, and human geography are combined with game theory, mathematical modelling* and computer simulation. Resting only on the assumption that people everywhere, at all times, were just people – with the same set of biological drives – we can hope to apply the full scientific method to the study of history. Combined with quantified historical and archeological evidence, there is the glimmering of a new renaissance in the study of history.

Across the intellectual divide, Civilization 4 (with somemodifications) is the most complete simulation we have for the processes that have shaped history. Although its remit is to be “just” a game, by exploring how the game unfolds we might learn something about how history itselfcould have unfolded. And we learn that we don’t understand all of the rules it followed. It is of great interest to understand a simulation model for the world that replays history as accurately as we can manage, without having to add too many of the specifics ourselves.

I first discussed these ideas when I decided to take the plunge and do some real research on the subject. Although I will link a lot to Wikipedia, most of the ideas are fully fleshed out in the references at the bottom.

It is about more than personalities: it is about having a real choice.

NB: Inspired by making the decision Cake or death? when the cake is a lie. Of course, it will still be politics and the cake will still be a lie, but we might hope for a slightly more appealing specials board.

This blog post discusses evidence that inheritance is, fundamentally, more important than upbringing in determining IQ. The original article is here. The results are striking: when a child is adopted from birth, the adopted parents IQ correlates with the child’s IQ until age 7. But by the teenage years, the correlation is gone – intelligent parents do not have intelligent adopted children, even though they do have intelligent biological children. The conclusion is difficult to avoid.

I don't want it to be true...

I have discussedIQ before, and it lead to quite strong disagreement with some knowledgeable people who somehow found my blog. This is (more) evidence – strong evidence – against the position I took in that discussion. The view – my view – that genetics should be ignored by society is weakened by these results. The truth is “obviously” the opposite – genetics do matter, a lot.

I can find some glimmers of hope – some possibilities that nurture may still win, despite the above evidence. But I doubt that the relative importance of nature and nurture will, in this particular case, be overturned. These are discussed at the end.

Like a good scientist, I am therefore going to change my mind and follow the evidence, right? Nope. I’m going to bloody mindedly stand by my opinion that genetics cannot (at least yet) play a role in decision making in society, even though by normal scientific standards it could be counted as a fact.

The scientist with a “non-scientific” view?

How can I possibly justify denying something that I believe to be true?

My reason is that, although we have enough scientific evidence about the effect of genetics on people, we do not have an understanding about the effect of acting on this knowledge. I am petrified by the thought of what decisions might be made on the basis of knowing IQ correlates better with nature than with nurture. Here are just two that could come about if the idea is accepted into the mainstream:

Intelligent, wealthy, middle classed people will be less likely to adopt from poor and/or unknown genetic stock. As discussed in the links above, it is not rational to adopt children who will not live up to expectations; instead, IVF and other solutions will be preferred. This could result in disaster for those needing adoption.

People who believe that they have good genetic stock would rationally want to “out breed” those with “inferior” genetics. In today’s class society, that would mean specifically preventing poor (or otherwise undesirable) people from breeding. We’ve seen this before, and it was not pretty.

Do we accept the evidence and put up with the consequences? I say no – although scientifically we can accept these results, they must not be accepted by society.

The responsible scientist

The correct response, I believe, is to place a stronger requirement on the evidence. Essentially, we need to know how to move from the society we have now, to a society that might exploit this knowledge, without causing chaos, misery and unfairness on the way. This requires several things: firstly, an almost unheard of degree of certainty in the scientific evidence that nature trumps nurture, because whilst there is even a glimmer of doubt any policy will be unfair. Secondly, it requires a strong understanding of the social response that people will have to such a policy. And thirdly, we must know how to deal with that in a way that is fair. (a fair rule: we would all agree to it before we know which side of the rule we will fall on.)

The high bar

My previous arguments on this subject focussed on the first of these points, because I’m not convinced that anyone knows anything about the second and third. The burden of proof must be with the nature camp, simply because the implications of it being true could be so dramatic. Therefore I will offer a couple of “get out” clauses to the above research.

Firstly, the results are averages over children that were either adopted or not. If there is a correlation with e.g. parents IQ and being adopted, then these results will be biased by it. (But that still assumes a genetic relationship for IQ, just a different one…)

Secondly, the results cannot account for the effect of “epigenetics“: that is (mostly), the effect of mothers health during pregnancy on the potential of her child. As I discussed previously, this effect is these days being seen as large (hence the “no alcohol” taboo for pregnant women…).

Thirdly, there may be social reasons that adopted children do poorly. If they are told they are adopted, then they may spend their teenage years in rebellion and doubt. If they are not told they are adopted, perhaps the parents still behave differently towards them.

Finally, as I discussed previously, if you assume a (false) social concept is true you may inadvertently make it come come about. People who are believed to have low “genetic IQ” might have low observed IQ – but only because society (and they themselves) expect it to be true.

The most important part of all – disclaimer

In all cases, it is extremely important to remember that these effects are small – they are simply correlations in a whole bunch of causes and effects. They do not predict what will happen for any given adoption, or indeed natural birth. Some children do well in terrible circumstances, and others fritter away privilege. Correlation does not imply causation. IQ does not measure anything other than IQ – and itself only weakly correlates with intelligence. What of happiness, life satisfaction, social responsibility, and so on?

See my previous posts and the comments therein for the references I collected on the subject: on race and IQ, and on the existence of races (accidentally about IQ).

This graph in the NY Times by Ed Easterling makes for fascinating reading for anyone who has any interest in dabbling in the stock market. It shows how much money you would have made/lost in real terms depending on when you invested. Although there is a trend to gain roughly 4% a year, the volatility of the stock market is gigantic: if you put in £10000 and didn’t touch it for 20 years, you could have lost 2% by the end, or gained 8%, all depending on when you invested. Investments post 2000 have been poor on average, but there are nice patterns of “boom/bust” that *if they continue into the future* would indicate that the next 20 years might be higher than normal. Or they might not; the stock market sucks that way!

In conclusion: don’t invest in the stock market if you need reliable returns in less than 40 years…